Solve the following multiplication problems.
a. 9 kg 3 hg 1 cg × 9 =
b. 11 dg 4 cg × 12 =
c. 10 g 5 dg × 6 =
d. 5 g 3 dg 4 cg × 8 =

help...

Answer: width = 30 m, length = 150 is one possible answer

Step-by-step explanation:

P = 2L + 2w                            A = L x w

  = 2(65) + 2(115)                       = 65 x 115

  = 130 + 230                            = 7,475

  = 360

360 ÷ 2 = 180

Find 2 numbers whose sum equals 180 and product is less than 7475

Sum: L + w = 180   ⇒   w = 180 - L

Product: Lw < 7475

Graph these 2 equations to see which coordinates of the sum fall into the shaded region of the product.

Answer:

We can not solve for a unique cost for each soldier.

Step-by-step explanation:

Let x be the daily cost for legionaries and y be the daily cost for archers.  

Upon using our given information we will get a system of linear equations as:

[tex]3x+3y=10...(1)[/tex]

[tex]x+y=3...(2)[/tex]

Now we will solve for x from our 2nd equation,

[tex]x = 3-y[/tex]

Now we will substitute this value in our 1st equation.

[tex]3(3-y)+3y=10[/tex]

[tex]9-3y+3y=10[/tex]

We can see that -3y cancels out with 3y  and 9 is not equal to 10. So this is an unsolvable system. Therefore, we can not find a unique cost for each soldier.

Answer: No solutions

Step-by-step explanation:

Set the polynomial equal to each other.

x2 - 2x - 5 = x3 - 2x2 - 5x - 9

Move all the terms to the right side of the equation to make the left side equal to zero.

0 = x3 - 3x2 - 3x - 4

Now we use synthetic division to factor.

4 |  1       -3        -3           -4

                4         4             4

___________________________

       1       1          1            0

0 = (x - 4)(x2 + x + 1)

Now you can set the factors equal to zero and solve for x.   Since the quadratic factor has no real solutions, we ignore and focus on the linear factor. x = 4

Evaluate any of the function when x=4 to get the y-coordinate of the intersection point.

Answer:

The answer is 0.8 so A

Step-by-step explanation:

Perimeter (P) = 2L + 2w

68 = 2L + 2w

68 - 2L = 2w

2(34 - L) = 2(w)

34 - L = w

********************                                

Area (A) = L * w

     240 = L (34 - L)

     240 = 34L - L²

L² - 34L + 240 = 0

(L - 10)(L - 24) = 0

L = 10  or  L = 24

w = 34 - L   = 34 - 10   = 24      or      w = 34 - 24   = 10

Answer: width = 10, length = 24  assuming length is bigger than the width

Perimeter (P) = 2L + 2w

68 = 2L + 2w

68 - 2L = 2w

2(34 - L) = 2(w)

34 - L = w

********************                                

Area (A) = L * w

     240 = L (34 - L)

     240 = 34L - L²

L² - 34L + 240 = 0

(L - 10)(L - 24) = 0

L = 10  or  L = 24

w = 34 - L   = 34 - 10   = 24      or      w = 34 - 24   = 10

Answer: width = 10, length = 24   assuming length is bigger than the width

In order to better find the points on this graph, we need to convert it from standard form to slope-intercept.

We can do that by solving for y.

-7y + 8 = 21x - 6

Subtract 8 from both sides.

-7y = 21x - 14

Divide both sides by -7

y = -3x + 2

Now that the equation is in slope-intercept, we can find two points on the line.

We know that (0, 2) will be the first point, because 2 is the y-intercept.

We can plug 1 into the x value of the equation to find the corresponding y value.

y = -3(1) + 2

y = -3 + 2

y = -1

The second point is (1, -1)

It's the linear function.

The slope-intercept form: y = mx + b.

-7y + 8 = 21x - 6      subtract 8 from both sides

-7y = 21x - 14     divide both sides by (-7)

y = -3x + 2

We need only two points:

for x = 0 → y = -3(0) + 2 = 0 + 2 = 2 → (0, 2)

for x = 2 → y = -3(2) + 2 = -6 + 2 = -4 → (2, -4)

Answer: (-∞, -4)

To find the interval(s) over which the function is constant,

We look at the graph and pick the interval where the graph is neither increasing nor decreasing

When the graph is neither increasing nor decreasing means it should be a straight line

From the given graph , we have a straight line starts at -4  and goes to infinity

So constant interval is (-∞, -4)

The function is constant over the interval [0, 20].

The function is constant when its graph is a horizontal line. In this case, the graph is a horizontal line between x = 0 and x = 20, inclusive. Therefore, the function is constant over the interval [0, 20].

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23 miles

hope this helps :)

If there is 45 angle from the south to the east α= 45° then the distance of d=32miles is

the diagonal of the square and your question how far south has it sailed is the side of the square let's call it x.

The relation is

d = x √2 => x= d/√2 = 32/1.41 ≈ 22.69 ≈ 22.7 miles

The correct answer is 22.7 miles

Good luck!!

To solve this, you first have to find the number of yards in one mile.

If three feet = 1 yard, and 5280 ft = 1 mile, all you have to do to find the number of yards in a mile is divide 5280 feet by 3 feet.

You end up with 1760 yards in 1 mile.

To find the number of yards in 2 miles, all you would have to do is multiply 1760 by 2

To convert 2 miles into yards, first change miles to feet (2 miles * 5,280 feet/mile = 10,560 feet). Then, convert feet to yards (10,560 feet ÷ 3 feet/yard = 3,520 yards). So, 2 miles is equal to 3,520 yards. therefore, option b is correct

To calculate the number of yards in 2 miles, we must first know the relationship between miles, feet, and yards. As the question mentioned, 1 mile = 5,280 feet and 1 yard = 3 feet.

So the first step is to convert 2 miles into feet: 2 miles * 5,280 feet/mile = 10,560 feet.

The second step is to convert feet into yards: 10,560 feet ÷ 3 feet/yard = 3,520 yards.

Therefore, there are 3,520 yards in 2 miles.

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The new dimensions are 6.75 inches by 9 inches

The dimensions of the new photo if, Sandra has a photo that is 9 inches by 12 inches, and The scale factor is 3 / 4, is 6.75 inches by 9 inches.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an object.

Given:

Sandra has a photo that is 9 inches by 12 inches,

The scale factor is, s = 3 / 4

Calculate the dimensions of the new photo as shown below,

The length = 9 × 3 / 4

The length = 27 / 4

The length = 6.75 inches,

The width of photo = 12 × 3 / 4

The width of the photo = 36 / 4

The width of the photo = 9 inches

Thus, the dimensions of the new photo will be 6.75 inches by 9 inches.

To know more about scale factors:

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When a function is reflected over the x-axis, the positive y-values become negative and the negative y-values become positive.

When a function is reflected over the x-axis, the positive y-values become negative and the negative y-values become positive. In the case of f(x)=2/3(6)^x, when it is reflected over the x-axis, the positive y-values will become negative and the negative y-values will become positive. This means that the range of the reflected function will be the opposite of the original range. Since the original range is all positive y-values, the reflected range will be all negative y-values.

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When Riley dove 8 feet further down from her initial position of 12 feet below sea level, her new location is 20 feet below sea level.

Riley was initially scuba diving 12 feet below sea level. This can be represented as a negative number, so we start with -12. Then, she dove 8 feet further down. In mathematical terms, this means we subtract another 8 from -12.
Thus, her elevation now is -12 - 8 = -20. Therefore, Riley is now 20 feet below sea level.

Hence, it is proved here completely.

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Vertical angles are opposite each other when two lines intersect and are equal. Linear pairs of angles are adjacent angles that form a straight line and their sum is always 180 degrees. The difference lies both in their position and their angle sum.

So, in sum, the difference lies in their positioning (vertical angles are opposite, linear pair angles are adjacent) and in their sum (vertical angles are equal, linear pair angles sum to 180 degrees).

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A) False because it is not a line (it is a parabola)

B) False  because it fails the horizontal line test

C) False because it passes the vertical line test.

D) True because it passes the vertical line test but fails the horizontal line test.

Answer: D

All we have to do here is multiply how many liters of water they drink in a day (225) by 2

225 x 2 = 450

Therefore, elephants drink 450 liters of water in 2 days

Hope this helps you

-AaronWiseIsBae

Tony and Mike, factored the trinomial [tex]8x^2 - 12x - 8[/tex]

Tony factored it as 4(x - 2)(2x + 1) and

Mike factored it as (x - 2)(8x + 4)

[tex]8x^2 - 12x - 8[/tex]

GCF is 4. We factor out 4

[tex]4(2x^2 - 3x - 2)[/tex]

2*-2=-4. We find out two factors whose product is -4  and sum is -3

two factors are -4  and 1. Split middle term -3x using two factors

[tex]4(2x^2 - 4x + 1x - 2)[/tex]

Group first two terms and last two terms

[tex]4[(2x^2 - 4x) + (1x - 2)][/tex]

Factor out GCF from each group

[tex]4[2x(x - 2) + 1(x - 2)[/tex]

4(2x+1)(x-2)

Tony factored it correctly

Mike factored it as (x − 2)(8x + 4)

Mike factor 8x+4 further. GCF of 8 and 4 is 4

So it becomes 4(2x+1)

Mike not factored it completely

Answer:

- Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet

- The ball rises by 16 in the first half second, but only 8 feet over the next one

- After it reaches 25 feet in the air, the ball drops

- The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.

Step-by-step explanation:

Let's rewrite the table:

Time (seconds) Height (feet)

0 0

0.5 16

1 24

1.25 25

1.5 24

2 16

2.5 0

By simply looking at the table, we can see that the following statements are all correct:

- Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet

- The ball rises by 16 in the first half second, but only 8 feet over the next one

- After it reaches 25 feet in the air, the ball drops

- The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.

Let's assume

independent variable is x

dependent variable is h

A linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases.

so, we can use formula of linear function

[tex]h=mx+b[/tex]

where

m is slope

[tex]m=-\frac{1}{5}[/tex]

now, we can plug values

[tex]h=-\frac{1}{5}x+b[/tex]

The value of the function at 0 is 3

so, at x=0 , h=3

we can use it and find b

[tex]3=-\frac{1}{5}*0+b[/tex]

[tex]b=3[/tex]

now, we can plug back

[tex]h=-\frac{1}{5}x+3[/tex]

now, we can draw graph

Graph:

Answer:The y-intercept is 3,The slope is [tex]-\frac{1}{5}[/tex],and the x-intecept is 15.

Step-by-step explanation: Credit:The answer is above me.

The answer is (C)

[tex]xy (x + 1), x(x+2)[/tex]

By multiplying x in equation

[tex]y(x^2 + x), x^2 + 2x[/tex]

[tex]y(x^2 + x), x(x+2)[/tex]

All the 4 factors are (x^2 + x), y, x, (x + 2)

So, the LCM is

[tex]xy(x + 1)(x + 2)[/tex]

Final answer:

The LCM of xy(x + 1) and x(x + 2) is found by including the highest powers of all variables and unique factors from both expressions, yielding x²y(x + 1)(x + 2).

Explanation:

The Least Common Multiple (LCM) of two algebraic expressions is the smallest expression that both original expressions can divide into evenly without leaving a remainder. To find the LCM of xy(x + 1) and x(x + 2), we look for the highest power of all the variables and factors included in both expressions.

The factor x appears in both expressions, but with different powers. The highest power of x in the given expressions is x² as seen in the second expression.

The factor y appears only in the first expression, so it must also be included in the LCM.

Next, the factors (x + 1) and (x + 2) are both unique, so they are also included in the LCM.

Therefore, the LCM of xy(x + 1) and x(x + 2) is x²y(x + 1)(x + 2), which corresponds to choice C. Hence, the correct answer is C.xy(x + 1)(x + 2).



The answer is C) 2h + 1

First i factored out the negative sign, then i split the second term into two terms, then i factored out the common terms and i got -(h + 7) (2h + 1).

Answer:

One of the factor is (2h+1)

Step-by-step explanation:

[tex]-2h^2-15h-7[/tex]

Take out negative sign in common

[tex]-(2h^2+15h+7)[/tex]

Now factor the parenthesis

To factor this , we find out two factors whose product is 14 and sum is 15

[tex]-(2h^2+h+14h+7)[/tex]

Break first two terms and last two terms

[tex]-(2h^2+h)+(14h+7)[/tex]

[tex]-h(2h+1)+7(2h+1)[/tex]

[tex](-h+7)(2h+1)[/tex]

[tex](7-h)(2h+1)[/tex]

One of the factor is (2h+1)

let

x-------> the number of Lucy's orders

y-------> the number of Sam's orders

z-------> the number of Bob's orders

we know that

[tex]x+y+z=72[/tex]----> equation A

[tex]z=3x[/tex]-----> equation B

[tex]x=8+y-----> y=x-8[/tex] -----> equation C

substitute equation B and C in equation A

[tex]x+(x-8)+3x=72\\ 5x=72+8\\ 5x=80\\x=16\\[/tex]

find z

[tex]z=3*16=48[/tex]

find y

[tex]y=x-8------> y=16-8=8[/tex]

therefore

the answer is

the number of Lucy's orders is [tex]16[/tex]

the number of Sam's orders is [tex]8[/tex]

the number of Bob's orders is [tex]48[/tex]

Multiplication time!

10^6 = 1,000,000

93 × 1,000,000 = 93,000,000

Hope this helps!!!

If 8 of the picks are orange, then 6 of the picks will be green

Answer: D

Step-by-step explanation:

   y = x² - 8x + 5

  -5                -5

y - 5 = x² - 8x           complete the square by adding [tex](\frac{-8}{2})^{2}[/tex] to both sides

y - 5 + 16 =  x² - 8x + 16      the right side is a perfect square:  (x - 4)²

y + 11 = (x - 4)²

    -11            -11

y        = (x - 4)² - 11

if you traveled at 40 mph you would go 240 miles in 6 hours. your answer is 40 mph

Answer:

As per the given condition:  Rodrigo has a ladder that is 13 ft long. The ladder is leaned against a vertical wall. The top of the ladder is 10.8 ft above the ground.

The Orientation of the ladder with the wall forms a right triangle.  

The ladder length is the hypotenuse of the triangle,

the distance between the ladder at ground level and the base of the wall is the horizontal leg of the triangle,

and the height of the ladder is the vertical leg of the triangle.

⇒ Height of the ladder = 10.8 ft and hypotenuse = 13 ft

Using sine ratio formula;

[tex]\sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse side}}[/tex]

Opposite side = height of the ladder = 10.8 ft and

Hypotenuse side = 13 ft.

then;

[tex]\sin \theta = \frac{10.8}{13} =0.830769230769[/tex]

or

[tex]\theta = \sin^{-1}(0.830769230769)[/tex]

Simplify:

[tex]\theta = 56.2^{\circ}[/tex] (nearest to tenth place)

Since, it is given that the angle the ladder makes with the ground needs to be 60 degree or less for safety purposes.

(a)

Yes, this ladder in a safe position.

as [tex]\theta = 56.2^{\circ} < 60^{\circ}[/tex]

(b)

You can see the diagram as shown below in the attachment.

3 × 4 × 3 - 2 × 4²

36 - 2 × 4²

36 - 2 × 16

36 - 32

The answer is 4

Is that right? I hoped it helped...